which end up being related to the Yukawa couplings between the physical scalars and quarks. In fact,
with the usual conventions (see for instance [1]}, [2]}), the Yukawa
Lagrangian for the physical fields may be written as
\(-\mathcal {L}_\mathrm {Y} &=&\frac{iA}{v}\, \left[ \bar{u} \left( N_u P_R - N_u^\dagger P_L \right) u+ \bar{d} \left( N_d^\dagger P_L - N_d P_R \right) d \right]\nonumber \\ & &+ \frac{h}{v}\, \bar{u} \left[\left( s_{\beta - \alpha } M_u - c_{\beta - \alpha } N_u^\dagger \right) P_L+ \left( s_{\beta - \alpha } M_u - c_{\beta - \alpha } N_u \right) P_R\right] u\nonumber \\ & &+ \frac{h}{v}\, \bar{d} \left[\left( s_{\beta - \alpha } M_d - c_{\beta - \alpha } N_d^\dagger \right) P_L+ \left( s_{\beta - \alpha } M_d - c_{\beta - \alpha } N_d \right) P_R\right] d\nonumber \\ & &+ \frac{H}{v}\, \bar{u} \left[\left( c_{\beta - \alpha } M_u + s_{\beta - \alpha } N_u^\dagger \right) P_L+ \left( c_{\beta - \alpha } M_u + s_{\beta - \alpha } N_u \right) P_R\right] u \nonumber \\ & &+ \frac{H}{v}\, \bar{d} \left[\left( c_{\beta - \alpha } M_d + s_{\beta - \alpha } N_d^\dagger \right) P_L+ \left( c_{\beta - \alpha } M_d + s_{\beta - \alpha } N_d \right) P_R\right] d\nonumber \\ & &+ \frac{\sqrt{2} H^+}{v}\,\bar{u} \left( N_u^\dagger V P_L - V N_d P_R \right) d+ \frac{\sqrt{2} H^-}{v}\, \bar{d} \left( V^\dagger N_u P_R- N_d^\dagger V^\dagger P_L \right) u\,,\) 
